| Reference : Alternate modules are subsymplectic |
| E-prints/Working papers : Already available on another site | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/10993/29140 | |||
| Alternate modules are subsymplectic | |
| English | |
Guerin, Clément  [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |
| Apr-2016 | |
| No | |
| [en] alternate modules ; Lagrangians ; Finite Abelian groups | |
| [en] In this paper, an alternate module $(A,\phi)$ is a finite abelian group $A$ with a $\mathbb{Z}$-bilinear application $\phi:A\times A\rightarrow \mathbb{Q}/\mathbb{Z}$ which is alternate (i.e. zero on the diagonal). We shall prove that any alternate module is subsymplectic, i.e. if $(A,\phi)$ has a Lagrangian of cardinal $n$ then there exists an abelian group $B$ of order $n$ such that $(A,\phi)$ is a submodule of the standard symplectic module $B\times B^*$. | |
| http://hdl.handle.net/10993/29140 | |
| This paper won't be submitted per-se. It proves a technical result with elementary methods. It is used in my work on centralizers in PSL(n,C). It will eventually become an appendix of this paper. | |
| https://arxiv.org/abs/1604.07227 |
There is no file associated with this reference.
All documents in ORBilu are protected by a user license.
